Stability Analysis of a Fractional-Order African Swine Fever Model with Saturation Incidence

Simple Summary African swine fever is an acute pig disease caused by a highly contagious virus, and so far no cure has been found. Killing live pigs in affected areas is still the most effective way to prevent the spread of the disease. However, this approach can have a devastating impact on a country's pig industry. Thus, it is necessary to implement strict biosafety prevention and control before the disease begins to spread. In order to further understand the transmission characteristics of the disease and develop effective prevention and control measures, a fractional-order African Swine Fever model with saturation incidence is constructed in this paper. This model, as an effective method to describe the laws of the objective world, is suitable for analyzing the problem of the continued spread or regression of diseases in areas where there are African Swine Fever outbreaks in the real world. Both theoretical analysis and numerical simulations show that timely and effective disinfection measures on pig farms are important to prevent the spread of the disease.Abstract This article proposes and analyzes a fractional-order African Swine Fever model with saturation incidence. Firstly, the existence and uniqueness of a positive solution is proven. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the local and global stability of disease-free equilibrium is studied using the LaSalle invariance principle. Next, some numerical simulations are conducted based on the Adams-type predictor-corrector method to verify the theoretical results, and sensitivity analysis is performed on some parameters. Finally, discussions and conclusions are presented. The theoretical results show that the value of the fractional derivative alpha will affect both the coordinates of the equilibriums and the speed at which the equilibriums move towards stabilization. When the value of alpha becomes larger or smaller, the stability of the equilibriums will be changed, which shows the difference between the fractional-order systems and the classical integer-order system.